Moore lost Alabama's Tuesday special Senate election by more than 20,000 votes.

"I think he should," Trump told reporters on the South Lawn of the White House on Friday morning. "He tried. I want to support, always, I want to support the person running. We need the seat. We would like to have the seat."

Bannon, the former White House chief strategist, was one of Moore's longest and most fervent supporters. He visited the state three times to campaign on his behalf, including a rally the night before the election. He told the campaign that Moore needs to concede, a source familiar with the conversation tells CNN.

But Moore, who only addressed his supporters briefly on election night, said Wednesday that late-counted ballots could change the results of the election and urged his supporters to "stand against those who would take from us our country."

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"In this race, we have not received the final count to include military and provisional ballots," Moore said in a video issued by his campaign. "This has been a very close race, and we are awaiting certification by the secretary of state."

Alabama Secretary of State John Merrill, who voted for Moore in the election, told CNN's Jake Tapper that it's highly unlikely that Jones would not be certified as the winner.

"There's not a whole lot of mistakes that are made," Merrill said. "The people of Alabama have spoken tonight. They've made their voice heard loud and clear. The most important thing to remember now is the process needs to be followed to ensure that the integrity, the safety, and security of the election is preserved."

Moore's decision also puts him at odds with most of his party. The Alabama Republican Party, which never dropped support for Moore despite the sexual assault allegations made against him, has declared Jones the winner. Republican Sen. Richard Shelby congratulated Jones on his victory, and Sen. Luther Strange, the temporarily appointed Republican whose seat Jones will be taking, has offered to help Jones with the transition.